Method, system, and program product for feedback control of a target system utilizing imposition of a periodic modulating signal onto a command signal

ABSTRACT

Feedback control of a target system is provided which utilizes the imposition of a periodic modulating signal onto a command signal of a controller. The command signal with the period modulating signal imposed thereon is input to the target system to be controlled. A response of the target system to a manifestation of the periodic modulating signal in the command signal is detected, and a feedback signal is produced from the detected response. The periodic modulating signal and the feedback signal are processed together to produce an error signal, and the command signal is modified in accordance with the error signal to drive the current state of the target system toward a desired state, wherein the periodic modulating signal facilitates control of the target system.

TECHNICAL FIELD

This invention relates in general to feedback control systems, and moreparticularly, to feedback control systems in which a periodic modulatingsignal is imposed onto a controller's command signal.

BACKGROUND OF THE INVENTION

Feedback control systems typically use sensors to measure states of thetarget system to be controlled by the control system. For example,optical sensors and Hall effect devices produce rotor position signalsin feedback control systems for brushless direct current motors.However, such sensors add cost and complexity to a system and may alsorequire maintenance from time to time to assure continued properoperation. Such sensors can also be a common point of failure in systemsunder feedback control.

As a result of the disadvantages of many sensor devices, sensorlessfeedback control systems, which are not based on direct sensing oftarget system states, are attractive for some applications. For example,the back electromotive force (EMF) generated by stator windings of abrushless DC motor as its magnetized rotor rotates can be detected andused to determine rotor position. The transitions in the resultingback-EMF signal indicate times at which the rotor is in known positions.

Existing feedback control systems drive the phase error, i.e. thedifference between a command signal and the target system's response tothe command signal, toward zero. Such a feedback control system is pointoptimized. However, rather than simply nulling the phase error andconverging to a single operating point, it would be advantageous for afeedback control system to be able to track an error signal function,which is the difference between the actual state and desired state ofthe system, in order to deliberately run the motor with a non-zero phaseerror. The present invention provides a feedback control technique whichprovides this capability.

SUMMARY OF THE INVENTION

The shortcomings of the prior art are overcome and additional advantagesare provided through the provision of a method of feedback controlutilizing the imposition of a periodic modulating signal onto a commandsignal of a controller. Pursuant to the method, the command signal withthe periodic modulating signal imposed thereon is input to a targetsystem to be controlled. A response of the target system to amanifestation of the periodic modulating signal in the command signal isdetected, and a feedback signal is produced from the detected response.The periodic modulating signal and the feedback signal are processedtogether to produce an error signal, and the command signal is modifiedin accordance with the error signal to drive the current state of thetarget system toward a desired state, wherein the periodic modulatingsignal facilitates control of the target system.

In an enhanced embodiment, the target system comprises a motor and amotor drive circuit. In this embodiment, a motor drive signal isgenerated based on the command signal with the periodic modulatingsignal imposed thereon, wherein the motor drive signal is an input usedto drive the motor. Also, the detecting further comprises measuring aback-EMF signal generated by the motor and extracting the motor'sresponse to the manifestation of the periodic modulating signal in thecommand signal from the back-EMF signal. In this embodiment, the currentstate of the motor comprises the actual rotational speed of the motor;while the desired state comprises the desired rotational speed of themotor.

Systems and computer program products corresponding to theabove-summarized methods are also described and claimed herein.

Additional features and advantages are realized through the techniquesof the present invention. Other embodiments and aspects of the inventionare described in detail herein and are considered a part of the claimedinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other objects, features, andadvantages of the invention are apparent from the following detaileddescription taken in conjunction with the accompanying drawings inwhich:

FIG. 1 illustrates one embodiment of a state control loop for a targetsystem utilizing feedback control, in accordance with an aspect of thepresent invention;

FIG. 2 illustrates one example of a servomotor system environment for aDC-motor, in accordance with an aspect of the present invention;

FIG. 3 illustrates one embodiment of the drive circuit of FIG. 2;

FIG. 4 illustrates ideal back-EMF waveforms for the three phases of athree-phase brushless DC motor;

FIG. 5 illustrates one of embodiment of the drive signals to each phaseof a three-phase brushless DC motor;

FIGS. 6 a and 6 b illustrate exemplary measured back-EMF signals for twobrushless DC motors operating as generators;

FIG. 7 illustrates an exemplary measured back-EMF signal for one phaseof a brushless DC motor being driven by a 10 kHz pulse-width modulationdrive signal;

FIG. 8 illustrates one embodiment of a speed control loop of aservomotor system, which utilizes an embodiment of the motor controllerof FIG. 2, in accordance with an aspect of the present invention;

FIG. 9 illustrates the instantaneous frequency spectrum of the back-EMFof a brushless DC motor and several signal waveforms as a function oftime for the motor controller embodiment of FIG. 8 for negative, zero,and positive phase error conditions; and

FIG. 10 illustrates a time sequence of the instantaneous frequencyspectrum of the back-EMF of a brushless DC motor and correspondingsamples of two signal waveforms for the motor controller embodiment ofFIG. 8.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 illustrates one embodiment of a state control loop for a systemutilizing feedback control, in accordance with an aspect of the presentinvention. Controller 120 generates control signal 122 to control atarget system 130 in accordance with the desired target system actionand an error signal 152. Additionally, controller 120 receives periodicsignal 112 from periodic signal generator 110, and a manifestation ofperiodic signal 112 is imposed on control signal 122. State measurementdevice 140 detects the target system's response 132 to control signal122 and derives feedback signal 142 from the detected response, wherefeedback signal 142 is a measure of the target system's response to themanifestation of periodic signal 112 imposed on control signal 122.Error signal processor 150 completes the state control loop bygenerating error signal 152 as a function of periodic signal 112 andfeedback signal 142. In another example of the embodiment of the statecontrol loop illustrated in FIG. 1, the desired target system action isindicated by a command signal, which is input to controller 120.

FIG. 2 illustrates one example of a servomotor system environment for aDC-motor, in accordance with an aspect of the present invention, as anexemplary system utilizing feedback control with a state control loop.Motor controller 210 generates command signal 212, which is an input todrive circuit 220. Drive circuit 220 produces motor drive signals whichdrive motor 230. In the embodiment illustrated in FIG. 2, motor 230 is abrushless DC motor having three stator phases (A, B, and C), and drivecircuit 220 produces phase A drive signal on phase A interface 222,phase B drive signal on phase B interface 224, and phase C drive signalon phase C interface 226 to drive phase A, phase B, and phase C of themotor, respectively.

The rotation of the motor's rotor induces a time-varying voltage acrossthe phase windings of the motor's stator as the poles of the rotor passby the stator windings. This induced voltage across each stator phasewinding, which results from the generating action of the motor, is knownas a “back electromotive force” or “back EMF”. The back EMFs for phasesA, B, and C of motor 230 can be detected on phase interface A 222, phaseinterface B 224, and phase interface C 226, respectively, by drivecircuit 220 and provided as input signals bemf-a 214, bemf-b 216, andbemf-c 218, respectively, to motor controller 210. The servomotor systemenvironment for a DC-motor illustrated in FIG. 2 can be used to drive aload such as a fan for example.

FIG. 3 illustrates one embodiment of drive circuit 220 of FIG. 2.Command signal 212 received from the motor controller is an input togate driver circuits 310, 312, and 314 for power transistor pairs 320,322, and 324, respectively. Each pair of power transistors drives astator phase of the motor. Motor drive signals are produced on phaseinterface A 222, phase interface B 224, and phase interface C 226 bypower transistor pairs 320, 322, and 324, respectively, which are drivenby gate driver circuits 310, 312, and 314, respectively. Resistivevoltage divider circuits 330, 332, and 334 coupled to phase interfacesA, B, and C, respectively, produce back-EMF signals bemf-a 214, bemf-b216, and bemf-c 218, respectively. Other means for detecting back-EMFsignals, known to those with ordinary skill in the art, may also be usedin accordance with the present invention.

FIG. 4 illustrates ideal back-EMF waveforms for the three phases of athree-phase brushless DC motor having two rotor poles. In this example,the period of ideal phase A back-EMF waveform 410 is equal to the timefor one rotation of the rotor (360 spatial degrees). The reference linecrossed by phase A back-EMF waveform 410 represents the voltage level ofelectrical neutral in the system. The transistor names and arrowsindicate the direction of current flow for the time intervalscorresponding to the back-EMF waveform segments. The ideal back-EMFwaveforms of FIG. 4 have trapezoidal shapes.

FIG. 5 illustrates one of embodiment of the drive signals to each phaseof a three-phase brushless DC motor having two rotor poles when themotor is driven to rotate at the same speed as is depicted in theback-EMF waveforms of FIG. 4. The features of the drive signal for phaseA are discussed in the following as an example. This drive signalcomprises positive pulse-width modulated pulses 510, which have positiveaverage level 520, for a time period corresponding to 120 degrees ofrotation followed by the neutral voltage level for a periodcorresponding to 60 degrees of rotation and negative pulse-widthmodulated pulses 511, which have negative average level 521, for a timeperiod corresponding to 120 degrees of rotation followed by the neutralvoltage level for a period corresponding to 60 degrees of rotation. Thetransistors, which are ON, are indicated for various time intervals, andthe arrows indicate the direction of current flow.

FIGS. 6 a and 6 b illustrate exemplary measured back-EMF signals for twobrushless DC motors operating as generators. Back-EMF waveform 610 ofFIG. 6 a and back-EMF waveform 620 of FIG. 6 b are measured back-EMFsignals detected in one stator phase of two different brushless DCmotors. Both back-EMF waveform 610 and back-EMF waveform 620 differ fromthe ideal trapezoidal back-EMF waveforms of FIG. 4, and they differ fromeach other. The deviation of back-EMF waveforms 610 and 620 from theideal trapezoidal back-EMF waveforms results from the fact that rotormagnets of the motors measured do not have linear flux gradients. It isalso apparent from FIGS. 6 a and 6 b that there is variation among theback-EMF waveforms generated by different motors. (It should be notedthat the flattened bottoms of back-EMF waveforms 610 and 620 areartifacts of the rectifying action of diodes included in the packagescomprising the power transistors of power transistor pairs 320, 322, and324. The actual back-EMF voltages produced by the motors areapproximately symmetrical.) The variations among measured back-EMFwaveforms and from the ideal back-EMF waveform cause noise in feedbackcontrol systems which are based on assumptions about the characteristicshape of the actual back-EMF generated by a spinning motor.

Another source of noise in the detected back-EMF signal in feedbackcontrol systems for brushless DC motors is the pulse-width modulatedmotor drive signal. One example of this type of motor drive signal forthree motor phases is shown in FIG. 5 as discussed previously. FIG. 7illustrates an exemplary measured back-EMF signal for one phase of abrushless DC motor being driven by a 10 kHz pulse-width modulation drivesignal. In FIG. 7, the superposition of the motor drive signalcomprising pulses similar to pulse-width modulated pulses 510 of FIG. 5onto the back-EMF generated by the motor is apparent in detectedback-EMF signal 710.

Because of the sources of noise in feedback control systems forbrushless DC motors which utilize motor back-EMF as a feedback signal,it is advantageous to impose a periodic modulating signal onto the drivesignal and to detect the motor's response to the imposed periodicmodulating signal so that the motor's response to the imposed periodicmodulating signal may be used as feedback in a closed loop controlsystem. FIG. 8 illustrates one embodiment of speed control loop 800 of aservomotor system, which utilizes an embodiment of motor controller 210of FIG. 2, in accordance with an aspect of the present invention. Theembodiment of motor controller 210 illustrated in the block diagram ofFIG. 8 utilizes a periodic modulating signal to facilitate theacquisition and maintenance of lock in the speed control loop embodimentillustrated in FIG. 8. This embodiment of motor controller 210 and theoperation of speed control loop 800 are described in more detail below.

As discussed previously with respect to FIG. 2, motor controller 210generates command signal 212, which is input to drive circuit 220 toproduce drive signals 222, 224, and 226 for motor phases A, B, and C,respectively. For clarity, only phase A drive signal 222 and theback-EMF detected by drive circuit 220 for phase A of the motor, bemf-a214, are shown in FIG. 8. In accordance with the embodiment of motorcontroller 210 illustrated in FIG. 8, the voltage level of bias signal816, which is the output of DC bias generator 815, is proportional tothe desired speed of the motor; bias signal 816 may vary over time inresponse to inputs received by DC bias generator 815.

In one embodiment of the present invention, periodic modulating signalgenerator 810 generates periodic modulating signal 811, which is inputDC bias generator 815. DC bias generator adds periodic modulating signal811 to the level of bias signal 816 that corresponds to the desiredrotational speed to effect an amplitude modulation of bias signal 816.In addition, error signal 871 from digital signal processor 850 is addedto bias signal 816 to drive the motor toward the desired rotationalspeed.

Voltage controlled oscillator (VCO) 820 receives bias signal 816(including the added periodic modulating signal and error signal) andgenerates a periodic clock signal 821 having an instantaneous frequencythat is proportional to the instantaneous voltage level of bias signal816. Transistor selector state machine 825 is clocked by clock signal821 received from the VCO 820 to generate command signal 212, which isinput to drive circuit 220. As a result, periodic modulating signal 811is imposed on command signal 212 from motor controller 210, and commandsignal 212 is also adjusted in accordance with error signal 871.

Drive circuit 220 produces phase A drive signal on phase A interface 222based on command signal 212. Although not illustrated in FIG. 8, drivecircuit 220 similarly produces drive signals for the other motor phaseson the corresponding motor phase interfaces. Drive circuit 220 alsodetects the back EMF generated by the motor on one motor phaseinterface, for example, phase interface A 222 as shown in FIG. 8. Theback-EMF detected on phase interface A 222, bemf-a 214, is fed back tomotor controller 210 as an input signal. Voltage scaler 830 amplifiesbemf-a 214 and outputs a scaled bemf-a signal to bandpass filter 835.Bandpass filter 835 has a center frequency that is approximately equalto the fundamental frequency of the back-EMF signal generated by themotor when it is operating at the desired speed. In other words, thecenter frequency of bandpass filter 835 is proportional to the desiredrotational speed of the motor's rotor. The passband of bandpass filter835 extends from approximately f_m Hz below this center frequency toapproximately f_m Hz above this center frequency, where f_m is thefundamental frequency of periodic modulating signal 811. Essentially,filtered bemf-a signal 836 produced by bandpass filter 835 comprises themotor's response to the manifestation of periodic modulating signal 811in the phase A drive signal on phase interface A 222. This filteredback-EMF signal is input to analog-to-digital converter (A/D) 840.Analog-to-digital converter 840 samples filtered bemf-a signal 836, andthe resulting filtered and sampled back-EMF signal is input to digitalsignal processor (DSP) 850.

Digital signal processor 850 comprises one embodiment of error signalprocessor 150 of the state control loop embodiment illustrated in FIG.1, and it generates error signal 871 as a function of the sampledperiodic modulating signal from analog-to-digital converter 845 and thefiltered and sampled back-EMF signal from analog-to-digital converter840. Digital signal processor 850 calculates the correlation between thesampled periodic modulating signal and the filtered and sampled back-EMFsignal, and then maps the correlation result to error signal 871. Themagnitude of error signal 871 computed by DSP 850 is proportional to thedifference between the desired state and the current state of the targetsystem. In one example, wherein the target system is direct-currentmotor and an associated motor drive circuit, the magnitude of errorsignal 871 is proportional to the difference between the desiredrotation speed of the motor and the actual rotational speed. The sign oferror signal 871 reflects whether the current state of the target systemis less than or greater than the desired state. In one example, whereinthe target system is direct-current motor and an associated motor drivecircuit, error signal 871 is positive if the actual rotational speed ofthe motor is less than the desired rotational speed, and error signal871 is negative if the actual rotational speed of the motor is greaterthen the desired rotational speed.

The structure of the processing by of digital signal processor 850 isdescribed in more detail in the following. The magnitude of the filteredand sampled back-EMF signal 841 from analog-to-digital converter 840adjusted by scaling logic 855 to produce a scaled feedback signal 856.Vector cross product calculator 860 calculates the vector cross productof scaled feedback signal 856 from scaling logic 855 and the sampledperiodic modulating signal from analog-to-digital converter 845 toproduce vector cross product signal 861. Vector cross product signal 861is filtered by lowpass filter 865, and the filtered vector cross productsignal from lowpass filter 865 is input to accumulator 870. The outputof accumulator 870 is input to mapping logic 880, which maps thecorrelation value output by accumulator 870 into error signal 871, whichis output by digital signal processor 850. Error signal 871 is input toDC bias generator 815 to close speed control loop 800.

In one example, mapping logic 880 utilizes the correlation value outputby accumulator 870 as an index to a look-up table, which stores samplesof error signal 871 corresponding to various values of the correlationvalue output by accumulator 870.

In digital signal processor 850 of FIG. 8, the processing of vectorcross product calculator 860 and accumulator 870 together effect thecorrelation calculation of the sampled periodic modulating signal withthe filtered and sampled back-EMF signal. Lowpass filter 865 attenuatesthe pulse-width modulation carrier noise in that is present in vectorcross product signal 861. The pulse-width modulation carrier noise maybe introduced into vector cross product signal 861 because somepulse-width modulation carrier component may remain in filtered bemf-asignal 836 produced by bandpass filter 835 due to the fact that it is amuch stronger signal than the back-EMF signal generated by the motor.

The frequency spectra and waveforms shown in FIGS. 9 and 10 illustratethe operation of speed control loop 800 in FIG. 8. FIG. 9 illustratesthe instantaneous frequency spectrum of the back-EMF of a brushless DCmotor together with an exemplary frequency response of bandpass filter835 and several signal waveforms as a function of time for the motorcontroller embodiment of FIG. 8 for negative, zero, and positive phaseerror conditions. More particularly, frequency spectrum 901, filteredback-EMF signal waveform 903, vector cross product signal waveform 904,and error signal waveform 905 are exemplary resulting waveforms for thenegative phase error condition. The corresponding periodic modulatingsignal waveform 902 is illustrated on the same time scale as filteredback-EMF signal waveform 903, vector cross product signal waveform 904,and error signal waveform 905 as a reference. Similarly, frequencyspectrum 911, filtered back-EMF signal waveform 913, vector crossproduct signal waveform 914, and error signal waveform 915 are exemplaryresulting waveforms for the zero phase error condition when periodicmodulating signal waveform 912 is imposed onto the command signal 212 ofFIG. 8. For the positive phase error condition, frequency spectrum 921,filtered back-EMF signal waveform 923, vector cross product signalwaveform 924, and error signal waveform 925 are exemplary resultingwaveforms when periodic modulating signal waveform 922 is imposed ontothe command signal. Filtered back-EMF signal waveforms 903, 913, and 923are examples of filtered bemf-a signal 836 for the negative, zero, andpositive phase error conditions, respectively; vector cross productsignal waveforms 904, 914, 924 are examples of vector cross productsignal 861 for the negative, zero, and positive phase error conditions,respectively; error signal waveforms 905, 915, and 925 are examples oferror signal 871 for the negative, zero, and positive phase errorconditions, respectively.

Note that when the phase error is zero, the output of bandpass filter835, filtered back-EMF signal waveform 913, has twice the frequency ofperiodic modulating signal waveform 912. This behavior can be explainedby the time sequence of the instantaneous frequency spectrum of theback-EMF of a brushless DC motor and corresponding sequences of periodicmodulating signal waveforms and filtered back-EMF signal waveformsillustrated in FIG. 10 for the motor controller embodiment of FIG. 8. InFIG. 10, the dots on periodic modulation signal waveforms 1011, 1012,1013, 1014, and 1015 and filtered back-EMF signal waveforms 1021, 1022,1023, 1024, and 1025 indicate the sampling times which correspond toinstantaneous frequency spectra of the back-EMF 1001, 1002, 1003, 1004,and 1005, respectively. From these time sequences of waveforms andspectra, it is apparent that the frequency spectrum of the back-EMFsignal passes through the peak of the frequency response of bandpassfilter 835 twice during one cycle of the modulating signal.

The discussion of the operation of speed control loop 800 in FIG. 8continues below with reference again to FIG. 9. In contrast to the zerophase error condition, when the phase error is either positive ornegative, this frequency doubling is not present in the filteredback-EMF signal, and filtered bemf-a signal 836 is either in phase(filtered back-EMF signal waveform 903) or out of phase (filteredback-EMF signal waveform 923) with the applied periodic modulatingsignal waveforms 902 or 922, respectively, which are sinusoidalwaveforms in the example illustrated in FIG. 9. The resulting vectorcross product signal waveform is therefore positive, zero, or negativefor the relative phase error conditions illustrated. However, acontinuum of waveforms exist for this signal for phase errors lyingbetween the illustrated examples. For these intermediate conditions,frequency doubling may exist during a part of the fundamental period ofthe vector cross product waveform.

Using the technique of the present invention, it is possible to lockvoltage controlled oscillator 820 in FIG. 8 to an arbitrary phase error.Speed control loop 800 generates a bipolar error signal with anamplitude that is proportional to the magnitude of the phase error; thisfeature can be used to control the VCO and to maintain any desiredamount of phase error in servomotor system.

It should be noted that the technique of the present invention doesrequire the peak of the bandpass filter's frequency response to be flat,as illustrated in FIGS. 9 and 10. Depending on the accuracy desired andthe amount of filter passband ripple, the feedback loop can be adjustedto track the phase error for any point in the passband of the bandpassfilter. Also, derivative signal processing techniques can be utilized ifthe bandpass filter's passband ripple is large enough to affect thephase error determination.

The vector cross product can be implemented with commercially availablecomponents, such as a digital four-quadrant multiplier using a Boothalgorithm, for example. The acquisition speeds of commercially availablemultipliers are sufficient for motor control applications, includingdriving cooling fans in computer systems. The method of the presentinvention can also be used to control a speed adaptive bandpass filterthat is tunable to match the current motor speed for improved noiseimmunity.

As would be appreciated readily by one with ordinary skill in the art,the foregoing describes several embodiments of a method, system, andprogram product for feedback control of a target system, wherein aperiodic modulating signal is imposed onto a command signal of acontroller. Pursuant to the method, the command signal with the periodicmodulating signal imposed thereon is input to a target system to becontrolled. A response of the target system to a manifestation of theperiodic modulating signal in the command signal is detected, and afeedback signal is produced from the detected response. The periodicmodulating signal and the feedback signal are processed together toproduce an error signal, and the command signal is modified inaccordance with the error signal to drive the current state of thetarget system toward a desired state, wherein the periodic modulatingsignal facilitates control of the target system.

In another embodiment, the target system comprises a motor and a motordrive circuit. In this embodiment, a motor drive signal is generatedbased on the command signal with the periodic modulating signal imposedthereon, wherein the motor drive signal is an input used to drive themotor. Also, the detecting further comprises measuring a back-EMF signalgenerated by the motor and extracting the motor's response to themanifestation of the periodic modulating signal in the command signalfrom the back-EMF signal. In this embodiment, the current state of themotor comprises the actual rotational speed of the motor; while thedesired state comprises the desired rotational speed of the motor. Themotor, motor drive circuit, and controller utilizing the feedbackcontrol method in accordance with the present invention comprise aservomotor system.

The present invention can be included in an article of manufacture(e.g., one or more computer program products) having, for instance,computer usable media. The media has therein, for instance, computerreadable program code means or logic (e.g., instructions, code,commands, etc.) to provide and facilitate the capabilities of thepresent invention. The article of manufacture can be included as a partof a computer system or sold separately.

Additionally, at least one program storage device readable by a machineembodying at least one program of instructions executable by the machineto perform the capabilities of the present invention can be provided.

The flow diagrams depicted herein are just examples. There may be manyvariations to these diagrams or the steps (or operations) describedtherein without departing from the spirit of the invention. Forinstance, the steps may be performed in a differing order, or steps maybe added, deleted or modified. All of these variations are considered apart of the claimed invention.

Although preferred embodiments have been depicted and described indetail herein, it will be apparent to those skilled in the relevant artthat various modifications, additions, substitutions and the like can bemade without departing from the spirit of the invention and these aretherefore considered to be within the scope of the invention as definedin the following claims.

1. A feedback control method for a target system to be controlled, saidmethod comprising: imposing a periodic modulating signal onto a commandsignal of a controller, the command signal with the periodic modulatingsignal imposed thereon being an input to a target system to becontrolled; detecting a response of the target system to a manifestationof the periodic modulating signal in the command signal and producing afeedback signal therefrom; processing the periodic modulating signal andthe feedback signal together to produce an error signal, wherein theprocessing comprises correlating the feedback signal with the periodicmodulating signal to produce a correlation value and mapping thecorrelation value to the error signal; and modifying the command signalin accordance with the error signal to drive a current state of thetarget system toward a desired state, wherein the periodic modulatingsignal facilitates control of the target system.
 2. The method of claim1, wherein: the correlating comprises calculating a vector cross productof the periodic modulating signal and the feedback signal to produce avector cross product signal, and integrating the vector cross productsignal to obtain the correlation value; and wherein the mappingcomprises utilizing a look-up table to convert the correlation value tothe error signal.
 3. A feedback control system for a target system to becontrolled, said system comprising: means for imposing a periodicmodulating signal onto a command signal of a controller, the commandsignal with the periodic modulating signal imposed thereon being aninput to a target system to be controlled; means for detecting aresponse of the target system to a manifestation of the periodicmodulating signal in the command signal and producing a feedback signaltherefrom; means for processing the periodic modulating signal and thefeedback signal together to produce an error signal, wherein the meansfor processing comprises means for correlating the feedback signal withthe periodic modulating signal to produce a correlation value and meansfor mapping the correlation value to the error signal; and means formodifying the command signal in accordance with the error signal todrive a current state of the target system toward a desired state,wherein the periodic modulating signal facilitates control of the targetsystem.
 4. The system of claim 3, wherein: the means for correlatingcomprises means for calculating a vector cross product of the periodicmodulating signal and the feedback signal to produce a vector crossproduct signal, and means for integrating the vector cross productsignal to obtain the correlation value; and wherein the means formapping comprises means for utilizing a look-up table to convert thecorrelation value to the error signal.
 5. At least one program storagedevice readable by a machine embodying at least one program ofinstructions executable by the machine to perform a feedback controlmethod for a target system to be controlled, said method comprising:imposing a periodic modulating signal onto a command signal of acontroller, the command signal with the periodic modulating signalimposed thereon being an input to a target system to be controlled;detecting a response of the target system to a manifestation of theperiodic modulating signal in the command signal and producing afeedback signal therefrom; processing the periodic modulating signal andthe feedback signal together to produce an error signal, wherein theprocessing comprises correlating the feedback signal with the periodicmodulating signal to produce a correlation value and mapping thecorrelation value to the error signal; and modifying the command signalin accordance with the error signal to drive a current state of thetarget system toward a desired state, wherein the periodic modulatingsignal facilitates control of the target system.
 6. The at least oneprogram storage device of claim 5, wherein: the correlating comprisescalculating a vector cross product of the periodic modulating signal andthe feedback signal to produce a vector cross product signal, andintegrating the vector cross product signal to obtain the correlationvalue; and wherein the mapping comprises utilizing a look-up table toconvert the correlation value to the error signal.